Simulation and verification of longitudinal chromatic aberration for optical system
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摘要: 现有的焦距检测方法通常由于检测仪器光源波长与光学系统不完全匹配从而产生纵向色差影响检测结果。针对这一问题，研究光学系统纵向色差的变化规律，并确定在400 nm～1 000 nm波段用于表示其函数关系的Conrady公式和复消色差特性公式。根据光学系统近焦位置的离焦量与位置呈线性关系的特性, 提出使用菲索干涉仪测量5种不同波长的焦距位置，获得单透镜和双胶合镜头的纵向色差曲线。实验结果表明: 在400 nm～1 000 nm波段单色系统和消色差系统的纵向色差的函数关系分别符合Conrady公式和复消色差特性公式，研究结果为焦距的理论计算和精确检测提供了新的思路和参考。Abstract: In ordinary focal length measurement, the measurement accuracy is usually affected by the longitudinal chromatic aberration because of the different design wavelengths between the optical system and the testing equipment. In order to solve this problem, the variation rule of longitudinal chromatic aberration for optical system was established, and the Conrady formula and apochromatic characteristic formula used to express the functional relationship of longitudinal chromatic aberration in the 400 nm~1 000 nm wavelength were determined. According to the linear relationship characteristic of the optical system between defocus amount of near-focus and position, the focal length position at 5 different wavelengths was measured by using Fizeau interferometer to obtain the longitudinal chromatic aberration curve of the single lens and the double cemented lens. Experimental results show that the longitudinal chromatic aberration function relationship of the monochromatic system complies with the Conrady formula, and the longitudinal chromatic aberration function relationship of the achromatic system matches the achromatic characteristic formula in the 400 nm~1 000 nm wavelength. The research provides new ways and references for the theoretical calculation and accurate detection of focal length.
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图 1 测量离焦位置的透射波前确定焦点位置原理
Figure 1. Focus determination by measuring transmitted wavefront of defocus position
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图 2 单色系统结构图与色焦移曲线
Figure 2. Monochromatic system structure and chromatic focal shift curve
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图 3 单色系统焦距-波长仿真曲线与Conrady公式求解曲线对比
Figure 3. Comparison of focal length wavelength simulation curve for monochromatic system with Conrady formula solution curve
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图 4 双高斯系统结构图与色焦移曲线图
Figure 4. Double Gauss system structure and chromatic focal shift curve
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图 5 双高斯系统的焦距-波长曲线与Conrady公式求解曲线对比
Figure 5. Comparison of focal length-wavelength curve for double Gauss system with Conrady formula solution curve
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图 6 确定复消色差特性公式幂级数系数范围流程图
Figure 6. Flow chart of determination of power series range for apochromatic characteristic formula
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图 7 双高斯系统的焦距-波长曲线与复消色差特性公式求解曲线对比
Figure 7. Comparison of focal length-wavelength curve for double Gauss system with apochromatic characteristic formula solution curve
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图 8 望远系统结构图和色焦移曲线
Figure 8. Telescopic system structure and chromatic focal shift curve
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图 9 望远系统焦距-波长曲线与求解复消色差特性公式曲线对比
Figure 9. Comparison of focal length-wavelength curve for telescopic system with apochromatic characteristic formula solution curve
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图 12 单色系统的Z3系数与位置曲线图
Figure 12. Curve of Z3 coefficient for monochrome system and position
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图 13 Conrady公式求解的单透镜后截距-波长曲线和数据残差图
Figure 13. Conrady formula solution curve of single lens and residual curve
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图 14 消色差系统Z3系数与位置的曲线图
Figure 14. Curve of Z3 coefficient for achromatic system and position
表 1 计算得到各波长焦点位置数据
Table 1 Focal position data of each wavelength
波长/nm 532 561 632.8 671 721 计算的后截距/mm 8.994 9.214 9.716 9.952 10.226 
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表 2 计算得到的各波长焦点位置
Table 2 Focal position of each wavelength
波长/nm 532 561 632.8 671 721 计算的后截距/mm 10.556 10.542 10.552 10.578 10.638
下载: 导出CSV
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